You can wrap them in archival paper before putting them in the bag.
edit: I had a thought. I think the only problem you might have with using the fabric bags and boxes is mice. They might chew it apart for nesting material. What I did, when I had to put some things in storage (not ponies but other 80/90s toys) was I put a small box in a larger box and placed moth balls in the space between them. So if something chewed into the outside box, it would be deterred from going after the inner box with my stuff in it.
Howe long are you going to store them? If it's going to be for a while, I would wrap the individual ponies in archival paper, also called museum paper. Put them in the bag, put that in a box, and put that box in a bigger box with the moth balls or whatever deterrent you want to use. Peppermint oil works to keep mice away too.